We report on the development of a Faraday rotation spectroscopy (FRS) instrument using a DFB diode laser operating at 2.8 µm for the hydroxyl (OH) free radical detection. The highest absorption line intensity and the largest gJ value make the Q (1.5) double lines of the 2Π3/2 state (υ = 1← 0) at 2.8 µm clearly the best choice for sensitive detection in the infrared region by FRS. The prototype instrument shows shot-noise dominated performance and, with an active optical pathlength of only 25 cm and a lock-in time constant of 100 ms, achieves a 1σ detection limit of 8.2 × 108 OH radicals/cm3.
© 2011 OSA
The hydroxyl (OH) free radical plays a critical role in atmospheric chemistry due to its high reactivity with volatile organic compounds (VOCs) and other trace species. Because of its very short life time (~1s or less) and very low concentration in the atmosphere (in the order of 106 cm−3), interference-free high sensitivity in situ OH monitoring by laser spectroscopy represents a real challenge [1,2]. To date, only two spectroscopic methods, florescence assay by gas expansion (FAGE) at low pressure and long-path differential optical absorption spectroscopy (DOAS), have been successfully employed for tropospheric OH measurement  with detection limits of ~105-106 radicals/cm3. However, FAGE system is rather complex, and several issues have been identified to affect the instrument performance, i.e.: interference of O3, Rayleigh scattering and laser scattering background, and the laser-generated artifact OH radicals with the UV laser (typically at 308 nm). DOAS operates in open path configuration, but long absorption pathlength (several kilometers) is needed in order to achieve necessary sensitivity for OH measurement. It is usually realized by multiple reflections (typically several hundred round-trip passes) of light beam between two mirrors separated by 10-40 m, which creates problem in optical alignment and makes airborne measurements difficult. In addition, interference from other atmospheric species is a serious issue that should be carefully addressed.
With respect to other spectroscopic methods a Faraday rotation spectroscopy (FRS) technique provides several advantages, which also meet the requirements for in situ detection of OH radicals. Those include: (1) the FRS relies on the particular magneto-optic effect observed for paramagnetic species, hence the major atmospheric species such as H2O, CO2, which are diamagnetic, do not produce any significant Faraday rotation effect; (2) with an appropriate design the FRS technique allows for measurements at the fundamental shot-noise limit, which significantly lowers the minimum detectable concentration limits for the target molecules. The measurement technique we used employs two nearly crossed polarizers with high extinction ratio. FRS signal is detected as modulation of intensity emerging from the second polarizer (analyzer) whose polarization axis is set at 90° + φ with respect to the polarization of the incident light (where φ is a small analyzer offset angle from the crossed position). This provides a significant reduction of the laser source noise; (3) when an AC magnetic field is used, the Zeeman splitting of the molecular absorption line (and thus the magnetic circular birefringence) is modulated. This provides an “internal modulation” of the sample, thus the external noise like interference fringes can be easily suppressed [3,4]. All these advantages make FRS capable of enhancing the detection sensitivity and mitigation of spectral interferences from diamagnetic species in the atmosphere, which is extremely important in measurement of highly reactive species such as OH radicals.
FRS spectrum of OH of the R (3.5) lines of the 2Π3/2 (υ = 1←0) state was first observed in 1980 by Litfin et al. . Pfeiffer et al.  reported in 1981 an OH detectivity of 1011 radicals/cm3 using FRS by probing the same OH lines. Both experiments used color center laser operating at 2.69 µm (~3708 cm−1). Progress since then in the development of compact and stable diode lasers as well as sensitive room temperature detectors permits one to further improve OH detection capabilities, which would make the FRS approach suitable for high accuracy atmospheric chemistry studies in environmental photoreactor chambers and for direct measurements of the total reaction rate of OH in atmospheric conditions. In this paper, we report on the development of an FRS instrument based on a distributed feed-back (DFB) diode laser operating at 2.8 µm (~3568 cm−1) for OH radical detection relevant to the environmental photoreactor chambers.
2. Experimental set-up
The experimental set-up used in the present work is schematically shown in Fig. 1 . A continuous-wave room temperature DFB diode laser operating at 2.8 µm (Nanoplus GmbH) was employed to probe Faraday rotation effects on the Q (1.5) double lines of OH. The laser temperature and current were controlled by a LDC 501 laser diode controller (Stanford Research System). A GPIB card was used to control the laser injection current in discrete steps. Laser wavelength was first calibrated using a wavenumber-current relationship based on an experimentally observed H2O absorption spectrum compared to the HITRAN 2004 database for line positions identification [7,8].
The output laser beam was first collimated by a 90° off-axis parabolic mirror (PM1) with an effective focal length (EFL) of 25 mm. The laser beam was then transformed into a quasi-parallel beam with a diameter of ~6 mm by using a combination of two AR-coated CaF2 lenses: F1 (f1 = 25 mm) and F2 (f2 = 50 mm). The 6 mm laser beam was directed to the FRS setup. A 38 cm long gas absorption cell (made of a quartz tube terminated with two CaF2, 1° wedged windows) located inside a 25 cm long solenoid was placed between two polarizers (with high extinction ratio of ξ < 5 × 10−6). The first linear polarizer is used to “clean-up” a polarization state of the laser radiation, and the second polarizer placed between the gas cell and a photodetector acts as a polarization analyzer. The solenoid was made of ~437 m (2323 turns) of a 16 gauge, enamel-coated copper wire wrapped around a 25 cm long PVC pipe. The pipe inner diameter was 5 cm with an out diameter of 6 cm. To operate the solenoid in AC mode, a series resonant RLC circuit with a resonant frequency fm of 1.302 kHz was constructed. A sine-wave voltage at fm from an internal sine generator in the phase sensitive lock-in amplifier (Signal Recovery 7270 DSP Lock-in), was amplified with an audio amplifier (RMX 1850HD) and subsequently used to modulate the magnetic field in the gas cell. The laser beam emerging from the analyzer was focused by a second parabolic mirror (PM2, EFL = 50 mm) onto a four-stage thermoelectrically cooled (HgCdZn)Te photovoltaic detector (Vigo PVI-4TE-3.4). The lock-in amplifier was used to demodulate the FRS signal at fm. The demodulated FRS signal from the lock-in was then digitalized and recorded with a laptop via a National Instruments data acquisition card (DAQ card, Model 6062E).
In our experiment, OH radicals were produced in a discharge cell by using a 2.45 GHz micro-wave (MW) discharge (Sairem Wavemat) in water vapor flow under low pressure (total pressure 0.5 – 1 mbar). The discharge cell was made of a 6 cm long quartz tube with an internal diameter of 4 mm. It was located in the center of the MW cavity and connected to the absorption cell (as shown in Fig. 1). The pure water vapor was produced by injecting distilled water from a sealed container into the discharge cell at a pressure below the saturated pressure. The temperature of the water container was kept at ~20 °C. The gas pressure was measured with two capacitance manometers: one for 1000 mbar scale (600AB Trans 1000MB, Edwards) and the other for 1 mbar full scale (655AB Trans 1MB, Edwards). A mass flow controller (GFC 17) was used to maintain the flow and provide a stable pressure inside the gas cell (typically 13 – 25 ml/min, the stability of the cell pressure was better than 0.01 mbar).
3. Results and discussion
There are three major noise sources in FRS including: (1) a detection system noise originating from a detector and amplifiers, which is independent of the optical intensity; (2) a laser source amplitude noise, proportional to the transmitted power; (3) a shot noise, proportional to the square root of the detected laser intensity. For small φ the laser power transmitted through the analyzer (and thus the laser noise) is proportional to ~φ 2, the shot noise is proportional to square root of the detected power thus being proportional to φ, while the detection system noise (including detector and preamplifiers noise) is constant and independent of φ. Given the FRS signal is proportional to φ, the FRS signal-to-laser noise varies as 1/φ, the signal-to-detection system noise improves proportionally to φ, and the signal-to-shot noise is independent of φ. Depending on individual contributions of each noise component the analyzer offset angle φ should be optimized to achieve an optimal signal-to-noise ratio (SNR). A detailed discussion of the FRS signal and noise sources was given in Ref . and references therein.
A series of measurements were performed to determine the noise sources and the optimum analyzer offset angle. The noise as a function of φ was measured with the lock-in amplifier at the first harmonic of the modulation frequency fm (Fig. 2 ). The measurement data were fitted with the following function:Fig. 2 with the Eq. (2) gives us: N 0 = 0.433 ± 0.019 μV Hz-1/2, N 1 = 4.897 ± 0.292 μV Hz-1/2, N 2 = 3.298 ± 1.152 μV Hz-1/2 (The actual extinction ratio of the polarizer of 6 × 10−4 was obtained from a separate measurement of the laser intensity vs. polarizer offset angle and it was fixed during the fit. The value of ξ is lower than polarizer specifications due to residual birefringence of the cell windows).
The fitted result of the detector noise is 433 nV Hz-1/2, which agrees very well with the direct measurement performed with a lock-in amplifier while the laser light is blocked (0.431 ± 0.009 μV Hz-1/2). Both results are in a good agreement with the detector manufacturer specification of 400 nV Hz-1/2. The fitted shot noise level is 1.4 times higher than the theoretical value deduced from , where q is the electron charge, I is the detector photocurrent, and G is the detector transimpedance (1.4 × 106 V/A, given by the manufacturer). Although the fitted result gives a satisfactory estimate for the shot noise we suspect several possible issues that could cause this term to be larger than the theoretical limit: (1) an underestimate of G given by the manufacturer as the measurement detector noise was also larger than specifications, (2) the actual measurement bandwidth for the lock-in amplifier settings might be larger than the value estimated based on the lock-in specification sheet, and (3) a detector non-linearity, which is quite common for thermoelectrically cooled MCT detectors; A small detector saturation non-linearity can transform part of the laser noise (a 2nd order effect with respect to an analyzer offset angle) to 1st order (linear) effect, which will be indistinguishable from the shot-noise contribution. Since both G as well as the bandwidth would need to be underestimated by a factor of 2 (which is unlikely) we suspect the detector non-linearity to be the strongest effect causing the shot-noise estimation difference. However it should be noted that this 40% difference in the shot-noise estimation will not have any considerable effect on the overall performance of the sensor that already shows a close to shot-noise limited operation.
For our system, the maximum SNR was achieved at analyzer offset angle of φ = 6°. As shown in Fig. 2, the total noise of the instrument at the optimum φ was 0.78 μV Hz-1/2, which corresponds to a minimum detectable Faraday rotation angle of 1.39 × 10−7 rad Hz-1/2. The instrument operates at only about 2.1 times the theoretical shot-noise level of 0.38 μV Hz-1/2. This clearly shows shot-noise-predominate operation of the sensor system.
To model the FRS signal, the R Δ that contains all the spectral information about the sample can be calculated as a sum of the spectral signals from all allowed transition components:Eq. (1), it is clear that the absorption intensity, the absorption pathlength, the analyzer offset angle and the number of allowed transition components are of importance in increasing FRS signal amplitude. Therefore it is essential to work with the transitions that provide the largest R Δ. For the Q branch, gJ' = gJ”, and all ΔM J = M J' - M J” = ± 1 components have the same magnetic modulation sensitivity dν/dB with opposite signs. The most efficient summation of all the transitions can be thus realized by the use of the Q branch for FRS [4,9]. In Fig. 3(a) , OH absorption line intensities in the infrared around 2.8 µm are given based on the HITRAN database . As can been seen, the Q (1.5e) and Q (1.5f) double-line intensities of the 2Π3/2 state at 3568.52382 cm−1 and 3568.41693 cm−1 are the strongest (9.556 and 9.553 × 10−20 cm−1/(molecule cm−2) at 296K respectively), they are 3 times stronger than those used in the previously reported OH detection using FRS at 3708 cm−1 (2Π3/2 R (3.5), υ = 1←0: 3.15 × 10−20 cm−1/(molecule cm−2) at 296K). The effective gJ value, geff, is the summation of all allowed transitions weighted by their transition probabilities, which determines the magnetic modulation sensitivity and the phase of the transition signal . A comparison of calculated geff values for the 2Π3/2 and 2Π1/2(υ = 1←0) states in the P, Q and R branches are shown in Fig. 3(b). The calculations of the gJ factors were based on the references [10,11] and the effective gJ value was calculated using Eq. (7) in the reference . The larger effective gJ values of the Q branch allow for achieving the maximum FRS signal using small magnetic fields. Though the small geff can be compensated with a large magnetic field to get a maximum SNR, large magnetic fields might cause problems in sensing applications (e.g. large cooling systems, excess electro-magnetic interference, etc).
In the present experiment, the OH free radical concentration was calibrated using direct absorption with wavelength modulation spectroscopy (WMS) based on a 2f detection scheme. A close-by H2O absorption line at 3568.79816 cm−1 (423 ← 432 of the υ1 band) allowed direct concentration measurement of the H2O vapor and cross-calibration of the OH radical concentration produced by MW discharge using the following equation [12,13]:7]. The 2f line-center peak amplitude was used in the present work for retrieving the absorber concentration, as it is weakly affected by the presence of amplitude modulation distortions in WMS. An example of wavelength modulation spectrum is shown in Fig. 4(a) . The spectra were acquired using a 4 Hz laser current ramp providing a frequency scan between 3568.3 and 3568.9 cm−1 and a 16 kHz wavelength modulation with a modulation depth of ~0.07 cm−1. A series of 2f spectra was recorded for different H2O concentrations (H2O vapor pressure) to generate a calibration curve showed in the insert of Fig. 4(a). With a MW discharge power of 75 W, OH concentration of 2.2 × 1012 radicals/cm3 was deduced using Eq. (4). A time series of the 2f data (over 1 hour) was recorded for the stability test of the MW discharge system. The relative variant (the ratio of standard deviation and mean value of the signal) of the OH signal was smaller than 1.6% so that the MW system was considered stable.
The FRS experiment was conducted under reduced pressure (0.6 mbar, optimized for efficient MW discharge). A series of experiments were performed to determine the optimum magnetic field strength B. The largest FRS signal was found at an AC solenoid current of 1.85 A, corresponding to B = 177 Grms (Gauss root-mean-square) measured inside the coil. Figure 4(b) shows an FRS spectrum of the Q (1.5e) and Q (1.5f) transitions of OH. The spectrum was measured with a lock-in time constant of 100 ms, fm set at 1.302 kHz, and analyzer offset angle φ = 6°. OH radicals were generated under the same experimental condition (water vapor flow rate, the position of discharge cell in the MW cavity, MW discharge power, the gas pressure in the discharge cell) as Fig. 4(a), yielding the same OH concentration. The measured 1σ noise level of 826 nV results in a bandwidth normalized system noise of 639.5 nV Hz-1/2 (comparable to the total noise of 780 nV Hz-1/2 obtained in Fig. 2). This translates into a 1σ (SNR = 1) detection limit of 8.2 × 108 OH radicals/cm3. The following parameters were used for simulation: [OH] = 0.95 × 1012 OH radicals/cm3, L = 25 cm, T = 296 K, B = 177 Gauss. The calculated lineshape agrees very well with the experimental data. Whereas the concentration used for simulation was about 2 times lower than the estimated value using 2f WMS calibration.
Several possible reasons have been considered for this discrepancy: an accuracy of the theoretical approximation of the FRS signal, a temperature-dependent absorption line intensity, the wall loss of OH radicals, and a non-uniformity of the magnetic field inside the coil. In the first case small differences are expected between the measurement values and the FRS model, which is based on a first order approximation of the lock-in signal amplitude with a simple difference between the Zeeman shifted dispersion profiles instead of a complete Fourier analysis of the signal generated by time varying magnetic field. In the second case, although the temperature of both the coil and the gas cell could vary during the experiment due to resistive heating of the coil, the temperature of the gas cell never exceeded ~32 °C (with active air cooling of the coil). Based on the HITRAN database, the line intensity decreases by about 4% for temperatures varying from 20 °C to 32 °C, which causes a negligible effect on the FRS signal. Another possible effect is the loss of about 5 × 109 OH radicals/cm3 per cm observed at the cell walls, which results in non-uniform distribution of OH concentration in the cell. As the OH radicals were generated at one end of the gas cell the magnetic field non−uniformity along the coil might become important. The magnetic field distribution measurement revealed that at both ends of the coil the magnetic field was by a factor of ~1.9 lower than in the coil center. Since the FRS simulation assumed constant value of B = 177 Gauss the non-uniformities in both the magnetic field and the OH concentration are likely to produce substantial discrepancies between the measurement and the model. Given the possibilities above as well as difficulties in OH radicals generation/sampling the factor of 2 difference between the model and the experimental data is acceptable at this stage of FRS OH sensor development. In the next design stage we plan to investigate the system calibration and sampling in more details.
In conclusion, in this paper we demonstrate performance of a prototype spectrometer for OH free radical detection using Faraday rotation spectroscopy. The highest absorption line strength and the largest gJ value make the Q (1.5) double lines of the 2Π3/2 state (υ = 1← 0) at 2.8 µm clearly the best choice for sensitive detection of OH in the infrared region by FRS using relatively low magnetic fields. A 1σ (SNR = 1) detection limit of 8.2 × 108 OH radicals/cm3 was achieved with an active optical pathlength of only 25 cm and a lock-in time constant of 100 ms. This demonstration was performed at reduced pressure due to the MW discharge method used for generation of OH radicals. In the final implementation the system can be used at any arbitrary pressure including atmospheric conditions (limited primarily by the maximum strength of magnetic field provided by the coil for optimum Zeeman splitting). The instrument shows high potential for future miniaturization required for field applications. In the final design we plan to implement long absorption pathlength to lower the minimum detection limit of the instrument and approach sensitivities required for the atmospheric OH monitoring. Based on a conservative estimate the detection sensitivity of ~107 radicals/cm3 can be attained which is suitable for high accuracy atmospheric chemistry studies in environmental photoreactor chambers and for direct measurement of total reaction rate of OH in the atmosphere .
This work is supported by the IRENI program of the Région Nord-Pas de Calais. W. Zhao thanks the IRENI program for the postdoctoral support and the Knowledge Innovation Foundation of the Chinese Academy of Sciences (KJCX2-YW-N24). The support of the Groupement de Recherche International SAMIA between CNRS (France), RFBR (Russia) and CAS (China) is acknowledged. G. Wysocki acknowledges the invited professorship support from the Université du Littoral Côte d’Opale and the US National Science Foundation (NSF) CAREER award CMMI-0954897. The authors thank Leveugle Francis for prompt technical help.
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